This *is* the travelling salesman problem! IIRC it's NP hard and as such the only way to get the 'best route' is by brute forcing it, that'll take a fair time though as there'd be 0.5*(n-1)! (43 589 145 600) possible routes, and that's if they're directly linked.
Can I have the post codes please, I wrote some software to do this as an artificial intelligence assignment at uni.